/export/starexec/sandbox2/solver/bin/starexec_run_its /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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WORST_CASE(?,O(n^1))  

Preprocessing Cost Relations
=====================================

#### Computed strongly connected components 
0. recursive  : [f1/7]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f300/4]
3. non_recursive  : [f1_loop_cont/5]
4. non_recursive  : [f2/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f1/7
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f1_loop_cont/5
4. SCC is partially evaluated into f2/4

Control-Flow Refinement of Cost Relations
=====================================

### Specialization of cost equations f1/7 
* CE 5 is refined into CE [8] 
* CE 4 is refined into CE [9] 
* CE 2 is refined into CE [10] 
* CE 3 is refined into CE [11] 


### Cost equations --> "Loop" of f1/7 
* CEs [10] --> Loop 8 
* CEs [11] --> Loop 9 
* CEs [8] --> Loop 10 
* CEs [9] --> Loop 11 

### Ranking functions of CR f1(A,B,C,E,F,G,H) 
* RF of phase [8]: [-A+B]

#### Partial ranking functions of CR f1(A,B,C,E,F,G,H) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    -A+B


### Specialization of cost equations f1_loop_cont/5 
* CE 7 is refined into CE [12] 
* CE 6 is refined into CE [13] 


### Cost equations --> "Loop" of f1_loop_cont/5 
* CEs [12] --> Loop 12 
* CEs [13] --> Loop 13 

### Ranking functions of CR f1_loop_cont(A,B,C,D,E) 

#### Partial ranking functions of CR f1_loop_cont(A,B,C,D,E) 


### Specialization of cost equations f2/4 
* CE 1 is refined into CE [14,15,16,17,18,19] 


### Cost equations --> "Loop" of f2/4 
* CEs [15] --> Loop 14 
* CEs [16,19] --> Loop 15 
* CEs [14,18] --> Loop 16 
* CEs [17] --> Loop 17 

### Ranking functions of CR f2(A,B,C,E) 

#### Partial ranking functions of CR f2(A,B,C,E) 


Computing Bounds
=====================================

#### Cost of chains of f1(A,B,C,E,F,G,H):
* Chain [[8],10]: 1*it(8)+0
  Such that:it(8) =< -A+B

  with precondition: [E=3,B>=A+1] 

* Chain [[8],9,11]: 1*it(8)+1
  Such that:it(8) =< -A+G

  with precondition: [E=2,B+1=F,B=G,B>=A+1] 

* Chain [[8],9,10]: 1*it(8)+1
  Such that:it(8) =< -A+B

  with precondition: [E=3,B>=A+1] 

* Chain [11]: 0
  with precondition: [E=2,A=F,B=G,A>=B+1] 

* Chain [10]: 0
  with precondition: [E=3] 

* Chain [9,11]: 1
  with precondition: [E=2,A=B,A+1=F,A=G] 

* Chain [9,10]: 1
  with precondition: [E=3,A=B] 


#### Cost of chains of f1_loop_cont(A,B,C,D,E):
* Chain [13]: 0
  with precondition: [A=2] 

* Chain [12]: 0
  with precondition: [A=3] 


#### Cost of chains of f2(A,B,C,E):
* Chain [17]: 0
  with precondition: [] 

* Chain [16]: 1
  with precondition: [B=A] 

* Chain [15]: 3*s(3)+1
  Such that:aux(2) =< -A+B
s(3) =< aux(2)

  with precondition: [B>=A+1] 

* Chain [14]: 0
  with precondition: [A>=B+1] 


Closed-form bounds of f2(A,B,C,E): 
-------------------------------------
* Chain [17] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [16] with precondition: [B=A] 
    - Upper bound: 1 
    - Complexity: constant 
* Chain [15] with precondition: [B>=A+1] 
    - Upper bound: -3*A+3*B+1 
    - Complexity: n 
* Chain [14] with precondition: [A>=B+1] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of f2(A,B,C,E): max([1,nat(-A+B)*3+1]) 
Asymptotic class: n 
* Total analysis performed in 117 ms.